The reliability function of a system or a piece of equipment at time t is define

Question

The reliability function of a system or a piece of equipment at time t is defined by R(4)- P(T1)1-F() where T, the failure time, is a random variable with a known distribution. A certain vacuum tube has been observed to fail uniformly over the interval t1, 21 (a) Determine the reliability of such a tube at time , tt2. (b) If 180i220, what is the reliability of such a tube at 200 h? (c) The failure or hazard rate function (t) is defined by -dRO R(t) (t)-1 F(t) R(t) Calculate the failure rate of this vacum tube. Interpret your result.

Explanation / Answer

Let T the failure time of a vacuum tube which is given to follow U(t1, t2), i.e.

f(t)         =            1/(t2-t1)   for          t1 < t < t2

The reliability function is given to be R(t) = 1-F(t)

R(t)        =            1-F(t)     =             1- (t-t1)/(t2-t1)                 for          t1 < t < t2

R(t) = 1- (t-t1)/(t2-t1) = 1-(200-180)/(220-180) = 1-20/40= 0.5

Hence 50 % component will survive by time t=200.

Hence in general at t=200 there will be chance of 0.05 that component will fail or 5% component will fail at time t=200.

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